Method for improved resolution of patterning using binary masks with pupil filters

ABSTRACT

A photolithography lens system is disclosed. The system has several elements all perpendicularly aligned to an optical axis. The elements include a light source that generates an exposing light, a first lens that has a front focal plane and a pupil plane, and a binary mask between the light source and the first lens. The binary mask is placed at the front focal plane of the first lens. A pupil filter is placed at the pupil plane. Finally, a second lens is provided that has a front focal plane at substantially the same position as the pupil plane. The second lens also has a back focal plane where a semiconductor wafer is placed.

FIELD OF THE INVENTION

The present invention relates to photolithography of semiconductordevices, and more particularly, to the use of a pupil filter inconjunction with a binary mask to improve resolution.

BACKGROUND INFORMATION

Photolithography is commonly used in a semiconductor manufacturingprocess to form patterns on a semiconductor wafer. In thephotolithography process, a photoresist layer is deposited over anunderlying layer that is to be etched. The photoresist layer is thenselectively exposed to radiation through a mask. The photoresist is thendeveloped and those portions of the photoresist that are exposed to theradiation are removed, in the case of “positive” photoresist.

The mask used to pattern the wafer is placed within a photolithographyexposure tool, commonly known as a “stepper”. In the stepper machine,the mask is placed between the radiation source and the wafer. The maskis typically formed from patterned chromium placed on a quartzsubstrate. The radiation passes through the quartz sections of the maskwhere there is no chromium substantially unattenuated. In contrast, theradiation does not pass through the chromium portions of the mask.Because radiation incident on the mask either completely passes throughthe quartz sections or is completely blocked by the chromium sections,this type of mask is referred to as a binary mask. After the radiationselectively passes through the mask, the pattern on the mask istransferred onto the photoresist by projecting an image of the mask ontothe photoresist through a series of lenses.

As features on the mask become closer and closer together, diffractioneffects begin to take effect when the size of the features on the maskare comparable to the wavelength of the light source. Diffraction blursthe image projected onto the photoresist, resulting in poor resolution.

One prior art method of preventing diffraction patterns from interferingwith the desired patterning of the photoresist is to cover selectedopenings in the mask with a transparent layer that shifts one of thesets of exposing rays out of phase, which will null the interferencepattern from diffraction. This approach is referred to as a phase shiftmask (PSM). Nevertheless, use of the phase shift mask has severaldisadvantages. First, the design of a phase shift mask is a relativelycomplicated procedure that requires significant resources. Secondly,because of the nature of a phase shift mask, it is difficult to checkwhether or not defects are present in the phase shift mask.

Another prior art approach is to use attenuated phase shift masks(AttPSM) to enhance resolution. The AttPSM has “leaky” chrome featuresthat are partially transmitting. Additionally, the light in the quartzregion is phase shifted by 180 degrees. The attenuated phase shift maskoperates by attenuating the zero order of light. However, onedisadvantage of attenuated phase shift masks is their cost ofmanufacture. Additionally, it has been found that attenuated phase shiftmasks can create an undesirable resist loss at the side lobes of thecontacts. The diffraction pattern of a square contact at the wafer,known as the Airy disk, consists of a main central intensity peak andsmaller secondary peaks that are offset from the main peak. When usingAttPSM, these secondary peaks are in phase with the background electricfield. The intensity resulting from the constructive interaction can besufficient to expose the resist, creating the undesired features knownas side lobes.

SUMMARY OF THE INVENTION

A photolithography lens system is disclosed. The system has severalelements all perpendicularly aligned to an optical axis. The elementsinclude a light source that generates an exposing light, a first lensthat has a front focal plane and a pupil plane, and a binary maskbetween the light source and the first lens. The binary mask is placedat the front focal plane of the first lens. A pupil filter is placed atthe pupil plane. Finally, a second lens is provided that has a frontfocal plane at substantially the same position as the pupil plane. Thesecond lens also has a back focal plane.

BRIEF DESCRIPTION OF DRAWINGS

The present invention will be described in conjunction with thefollowing drawings, wherein:

FIG. 1 is a schematic diagram of a prior art lens system for exposing asemiconductor wafer during photolithography.

FIG. 2 is a schematic diagram of a lens system for exposing asemiconductor wafer during photolithography formed in accordance withthe present invention.

FIG. 3 is illustration of a pupil filter formed in accordance with thepresent invention.

FIG. 4 is a graph of the transmissivity characteristics of the pupilfilter of FIG. 3.

FIG. 5 is a schematic illustration of a three slit pattern.

FIG. 6 is a schematic illustration of a two-dimensional hole pattern.

DETAILED DESCRIPTION OF THE INVENTION

The present invention uses a first focusing lens, a pupil filter, and asecond focusing lens to produce an image of a binary mask pattern withsharper defined edges on a semiconductor wafer. Additionally, the term“binary mask” refers to those masks that only have regions that aresubstantially opaque and regions that are substantially transmissive.The light emitting from a light source passes though the binary mask,the first lens, the pupil filter, and the second lens, and then projectsan image of the binary mask pattern onto the semiconductor wafer. Thefirst lens produces a Fourier-transformed image of the mask pattern. Thepupil filter selectively adjusts the amplitude of theFourier-transformed image to produce an “attenuated Fourier-transformed”image. The second lens produces an inverse-Fourier transformed image ofthe attenuated Fourier-transformed image, which is then projected ontothe wafer. As will be described below in more detail, theinverse-Fourier transform of the attenuated Fourier-transformed image isan accurate replica of the original mask pattern with sharply definededges.

When the openings of a mask that defines the mask pattern havedimensions comparable to the wavelength of the light source, diffractionwill occur when the light passes through the openings on the mask andonto the wafer. One example of such an opening is a contact hole, whichis square on the mask, but due to diffraction, the image of the openingformed on the wafer is blurred at the edges and prints as a roundfeature. The light intensity will be higher near the center of the slitimage, decreasing gradually at the edges. Thus, the boundaries of theimage of the opening at the wafer will not be clearly defined.

Fourier Analysis

Referring to FIG. 1, a light source 101, a first lens 103, and a secondlens 105 are aligned along the optical axis 107 of the lenses 103 and105. The focal lengths of the first lens 103 and the second lens 105 areboth equal to f. An object plane 109 is situated at the front focalplane of the first lens 103. The front direction refers to the directiontowards the light source 101. A pupil plane 111 is situated at the backfocal plane of the first lens 103. The pupil plane 111 is also situatedat the front focal plane of the second lens 105. An image plane 113 issituated at the back focal plane of the second lens 105. As seen in FIG.1, the distance between the object plane 109 and the center of the firstlens 103 is f, the distance between the center of the first lens 103 andthe pupil plane 111 is f, and the distance between the pupil plane 111and the center of the second lens 105 is f. Finally, the distancebetween the center of the second lens 105 and the image plane 113 isalso f.

For purpose of illustration, assume that the x-axis is the horizontalaxis (in the direction into the Figure), the y-axis is the verticalaxis, and the z-axis is the optical axis 107. A two-dimensional patternu(x, y) is placed at the object plane 109. According to Fourier opticstheory, the image formed at the pupil plane 111 is the two-dimensionalFourier transform of u(x, y), which is represented by U(fx, fy). Theintensity, U²(fx,fy), is referred to as the Fraunhofer diffractionpattern. The symbols fx and fy represent the coordinates on the pupilplane 111. The relationship between the u(x, y) and U(fx, fy) can bewritten as (Eq. 1):

U(fx, fy)=F[u(x, y)]

The notation F[ ] represents the Fourier transform operator.

When the image U(fx, fy) passes through the second lens 105 and isprojected on the image plane 113, the image at the image plane 113 willbe the inverse-Fourier transform of the image formed at the pupil plane111. If nothing is placed at the pupil plane 111 to alter the amplitudeand phase of the image at pupil plane 111, then the image projected onthe image plane 113 is nominally the original pattern u(x, y). This isbecause the inverse-Fourier transform of a Fourier-transformed image isthe same image itself. This can be written as:

F ⁻¹ [F[u(x, y)]]=u(x, y)

The notation F⁻¹[ ] represents the inverse-Fourier transform operator.In reality, due to the finite size of lenses, not all of the diffractionorders (Fourier modes) in the pupil plane can be collected. Hence, theimage does not exactly match the object.

Photolithography Using Pupil Filter in the Spatial Frequency Plane

Turning to FIG. 2, a schematic illustration of an embodiment of thepresent invention is shown. A photolithography system 201 includes alight source 203, a binary mask 205, a first lens 207, a pupil filter211, a second lens 209, and a wafer 213 that are all aligned along theoptical axis 215. The mask 205, first lens 207, pupil filter 211, secondlens 209, and the wafer 213 are placed perpendicularly to the opticalaxis 215. The light source 203 is typically an ultraviolet (UV) or deepultraviolet (DUV) light source, although it may be any type of radiationsource normally used in photolithography. An example of the light source203 is a KrF laser emitting DUV radiation with a wavelength of 248 nm.All components of FIG. 3, except for existence and placement of thepupil filter 211, are of conventional design for many photolithographystepper machines.

The binary mask 205 is typically formed of deposited chromium on quartzin accordance with conventional techniques. The binary mask 205 carriesa mask pattern 330 that is to be imprinted onto the wafer. The wafer 213is typically coated with a photoresist layer, so that after thephotolithography process, a replica of the mask pattern 330 is formed onthe photoresist layer on the wafer 213. The binary mask 205, the firstlens 207, the pupil filter 211, the second lens 209, and the wafer 213are mounted on a support frame of the photolithographic machine that isnot shown in the FIG. 2.

The focal length of the first lens 207 and the second lens 209 are equalto f. The binary mask 205 is situated between the light source 203 andthe first lens 207. The first lens 207 has two focal planes. The frontfocal plane 217 of the first lens 207 is defined to be the one that iscloser to the light source 203, and the back focal plane is defined tobe the one that is farther away from the light source 203. Likewise, thesecond lens 209 has two focal planes. The front focal plane of thesecond lens 209 is defined as the one that is closer to the light source203, and the back focal plane 219 is defined as the one that is fartheraway from the light source 203. In this embodiment, the back focal planeof the first lens 207 coincides with the front focal plane of the secondlens 209, and is called the pupil plane 221. This is because the imageformed at the back focal plane of the first lens 207 is the Fouriertransform of the image at the front focal plane 217.

In operation, light from the light source 203 passes through the binarymask 205, passes through the first lens 207, the pupil filter 211, thesecond lens 209, and then projects an image upon the wafer 213. Thefirst and second lenses 207 and 209 are conventional focusing opticallenses commonly used in many of the photolithography machines. Thecenter of the pupil filter 211 is situated at the pupil plane 221. Thewafer 213 is situated at the back focal plane 219 of the second lens209.

Preferably, the pupil filter 211 is formed using conventionaltechniques. For example, the paper “Optimization of Pupil Filters forIncreased Depth of Focus”, by von Bunau et al., Jpn. J. Appl. Phys.,Vol. 32 (1993) pp. 5350-5355 discusses various methods of manufacturingpupil filters. Specifically, for a circularly symmetric transmissionpattern, as discussed in the von Bunau paper, one method is to evaporatea metal film through a stencil mask onto a rotating substrate.

Being located at the pupil plane 221, the pupil filter 211 acts directlyon the spectral components of the image of the binary mask 205 toredistribute the relative intensities of the diffraction orders.Specifically, the pupil filter 211 acts to suppress the zero and firstorder of light emerging from said binary mask 205. The present inventionattempts to emulate the effect of an attenuated phase shift mask,without the cost and other disadvantages of the attenuated phase shiftmask.

Thus, the pupil filter 211 working in conjunction with the binary mask205 should have the same effect as an “attenuated phase shift maskversion” of the binary mask 205. In other words, the pupil filter 211and the binary mask 205 should be equivalent to the binary mask 205converted using conventional techniques into an attenuated phase shiftmask. In mathematical terms:

[Binary Mask]×[Pupil Filter]=AttPSM

or

 Pupil Filter=AttPSM/[Binary Mask]

From the above equation, the design of the pupil filter 211 requires theanalysis of the Fraunhofer diffraction pattern of the binary mask andthe AttPSM. The following expression gives the electric field at thepupil plane 221 of a single slit of width “2a” for a conventional binarymask, mask transmission function F(x)=2a,

U(p)=C ₁ ƒF(x)e ^(−ikpx) dx=C ₁×2 a sin c(kpa),

where sin c(ξ)=sin(ξ)/ξ, k=2π/λ, and p=ξNA/f(NA=Numerical aperture ofthe lens, f=focal length).

For AttPSM, the analysis is extended for a repeated 3 slit pattern whosetransmission amplitude and phase are given by A¹⁻³ and φ¹⁻³,respectively. The width of the center slit is 2a and the widths of theadjacent slits are (b−a) (see FIG. 5). Thus,${U(P)} = {C_{1}{\begin{bmatrix}{{\left( {b - a} \right)A_{1}^{\quad \varphi_{1}}^{\quad {{kp}{(\frac{a + b}{2})}}}{sinc}\quad \left( {{{kp}\left( {b - a} \right)}/2} \right)} +} \\{{{2a\quad A_{2}^{\quad \varphi_{2}}{sinc}\quad ({kpa})} +}\quad} \\{\left( {b - a} \right)A_{3}^{\quad \varphi_{3}}^{{- }\quad {{kp}{(\frac{a + b}{2})}}}{sinc}\quad \left( {{{kp}\left( {b - a} \right)}/2} \right)}\end{bmatrix}}}$

For AttPSM, A₁=A₃, φ₁=φ₃=π(180° C.), A₂=1, φ₂=0. Hence, the aboveexpression can be simplified to give the electric field of thediffracted mask pattern at the pupil plane 221 as a function of maskparameters: pitch (2b), feature size (2a), background transmissionamplitude A₁, and the exposure wavelength ( ).

AttPSM U(P)=C ₁×[2a sin c(kpa)−2(b−a)A ₁ sin c(kp(b−a)/2)cos(kp(a+b)/2)]

Using the above equations, the pupil filter 211 to be used with binarymask 205 to give a diffraction pattern that closely approximates theattenuated phase shift mask version of the binary mask 205 can beobtained explicitly in terms of mask and stepper parameters as:

[Binary Mask]×[Pupil Filter]=AttPSM

or

Pupil Filter=AttPSM/[Binary Mask]

∴Pupil Filter=1−{[2(b−a)A ₁ sin c(kp(b−a)/2)cos(kp(a+b)/2)]/2 a sinc(kpa)}

For a two dimensional (holes instead of slits) representation of theAttPSM (as shown in FIG. 6), the electric field is given by:${U(P)} = {C_{1}\begin{Bmatrix}{2c\quad {sinc}\quad {({kqc})\left\lbrack {{2a\quad {sinc}\quad ({kpa})} -} \right.}} \\{\left. {2\left( {b - a} \right)A_{1}{sinc}\quad \left( {{{kp}\left( {b - a} \right)}/2} \right)\cos \quad \left( {{{kp}\left( {a + b} \right)}/2} \right)} \right\rbrack -} \\{2b\quad {sinc}\quad {({kpb})\left\lbrack {A_{1}2\left( {d - c} \right){{sinc}\left( {{{kq}\left( {d - c} \right)}/2} \right)}\cos \quad \left( {{{kq}\left( {c + d} \right)}/2} \right)} \right\rbrack}}\end{Bmatrix}}$

Hence, the equivalent pupil filter is${2a\quad {sinc}\quad ({kpa})\quad 2\quad c\quad {sinc}\quad ({kqc}) \times {PF}} = {{\begin{Bmatrix}{2c\quad {sinc}\quad {({kqc})\left\lbrack {{2a\quad {sinc}\quad ({kpa})} -} \right.}} \\{\left. {2\left( {b - a} \right)A_{1}{sinc}\quad \left( {{{kp}\left( {b - a} \right)}/2} \right)\cos \quad \left( {{{kp}\left( {a + b} \right)}/2} \right)} \right\rbrack -} \\{2b\quad {sinc}\quad {({kpb})\left\lbrack {A_{1}2\left( {d - c} \right)\quad {{sinc}\left( {{{kq}\left( {d - c} \right)}/2} \right)}\cos \quad \left( {{{kq}\left( {c + d} \right)}/2} \right)} \right\rbrack}}\end{Bmatrix}\therefore{PF}} = {1 - \left\lbrack {A_{1}\frac{\left( {b - a} \right)}{a} \times \frac{{sinc}\quad \left( {{{kp}\left( {b - a} \right)}/2} \right)\cos \quad \left( {{{kp}\left( {a + b} \right)}/2} \right)}{{sinc}\quad ({kpa})}} \right\rbrack - {\left\lbrack {\frac{A_{1}{b\left( {d - c} \right)}}{a\quad c} \times \frac{{sinc}\quad ({kpb})\quad {sinc}\quad \left( {{{kq}\left( {d - c} \right)}/2} \right)\cos \quad \left( {{{kq}\left( {c + d} \right)}/2} \right)}{{sinc}\quad ({kpa})\quad {sinc}\quad ({kqc})}} \right\rbrack}}}$

Typically for contacts, c=a, and d=b. Therefore, $\begin{matrix}{{\therefore{PF}} = \quad {1 - \left\lbrack {A_{1}\frac{\left( {b - a} \right)}{a} \times \frac{{{sinc}\left( {{{kp}\left( {b - a} \right)}/2} \right)}\cos \quad \left( {{{kp}\left( {a + b} \right)}/2} \right)}{{sinc}({kpa})}} \right\rbrack -}} \\{\quad \left\lbrack {\frac{A_{1}{b\left( {b - a} \right)}}{a^{2}} \times \frac{{{sinc}({kpb})}\quad {{sinc}\left( {{{kq}\left( {b - a} \right)}/2} \right)}\cos \quad \left( {{{kq}\left( {a + b} \right)}/2} \right)}{{{sinc}({kpa})}\quad {{sinc}({kqa})}}} \right\rbrack}\end{matrix}$

This equation defines how the electric field of a conventional binarymask is modulated in the pupil plane when using AttPSM. The same fieldmodulation can be achieved using a conventional binary mask andmodulating the transmission and phase directly in the pupil planethrough a pupil filter. The equation for PF defmes the transmission andphase of the filter at all points (p,q) in the pupil plane to achievethe modulation imparted by the AttPSM.

Since the diffraction patterns of the mask pattern for the pupil filterand AttPSM are identical by design, the resolution enhancements topatterning are also identical. By substituting values for a (half widthof feature), b (half period), and A₁ (transmission amplitude of thebackground) in the equation above for the pupil filter, a pupil filterequivalent to an AttPSM can be obtained. A variety of pupil filters canbe designed for various combinations of a, b, and A1. This analyticaltechnique gives a method of parameterizing the family of pupil filtersto find an optimum for the desired configuration.

Using the above formula, it has been found that the PF for an isolatedfeature (b>>a) has a phase and transmittance variation. It is desirableto have a pupil filter without any phase change since phase defects addto lens aberrations and the filters are also difficult to manufacture.The pupil filter for a tightly nested feature where b˜2a is a puretransmittance filter (no phase change) which results in resolutionenhancement through the suppression of the zero order light In somecases the absolute value of PF can be >1. This is not physicallypossible. PF is then scaled so that the maximum transmittance is 1. Thiswill result in a difference in the peak image intensity for the binarymask+PF vs. the equivalent AttPSM which the PF was meant to mimic.

FIG. 3 illustrates an exemplary pupil filter 211 formed in accordancewith the present invention. FIG. 4 shows a graph illustrating thetransmissivity of the pupil filter 211 relative to radial position offof the optical axis 215. As can be seen, the central area of the pupilfilter 211 is more opaque to the irradiating light than the periphery.In FIG. 4, the radial position is measured in units of λ/NA, where NA isthe numerical aperture of the first lens 207. The amplitude scale ofFIG. 4 is scaled to have a value of 1.0 for complete tranmissivity and0.0 for complete opaqueness. The graph of FIG. 4 is taken directly fromcalculated data where A₁=0.4242 (18% transmission intensity), b=110 nm,a=55 nm. The image produced at the back focal plane of the first lens207 is the Fourier transform of the image at the front focal plane 217.Assuming that the thickness of the pupil filter 211 is small comparedwith the focal length f, the image projected onto the front end of thepupil filter 211 is the Fournier-transformed image of the mask patternof the binary mask 205. The pupil filter 211 selectively changes theamplitude of the Fourier-transformed image, and produces an “attenuatedFourier-transformed” image of the mask pattern. The image formed on theback focal plane 219 of the second lens 209 is the inverse-Fouriertransform of the image at the front focal plane of the second lens 209.Thus, the image projected onto the wafer 213 is the inverse-Fouriertransform of the attenuated Fourier-transformed image of the maskpattern.

Assume the mask 205 has a two-dimensional mask pattern 330 that isdescribed as u(x, y). The image u(x, y) is situated at the front focalplane 217 of the first lens 207. The Fourier-transformed image at thefront end of the pupil filter 211 is U₀(f_(x), f_(y)), where fx, fy arethe coordinates on the spatial frequency plane. The image formed afterpassing through the pupil filter 211 is U₁(fx, fy).

The pupil filter 211 is near the front focal plane of the second lens209 (under the assumption that the thickness of the pupil filter 211 issmall compared with the focal length f). The image projected on the backfocal plane 219 is the inverse Fourier transform of the image at thefront focal plane of the second lens 209. Therefore, the combination ofthe first lens 207, pupil filter 211, and second lens 209 has the effectof transferring the image of the mask pattern 330 onto the wafer 213with the edges more sharply defined. The blurring due to diffraction isreduced accordingly.

The above description of illustrated embodiments of the invention is notintended to be exhaustive or to limit the invention to the precise formsdisclosed. While specific embodiments of, and examples for, theinvention are described herein for illustrative purposes, variousequivalent modifications are possible within the scope of the invention,as those skilled in the relevant art will recognize.

These modifications can be made to the invention in light of the abovedetailed description. The terms used in the following claims should notbe construed to limit the invention to the specific embodimentsdisclosed in the specification and the claims. Rather, the scope of theinvention is to be determined entirely by the following claims, whichare to be construed in accordance with established doctrines of claiminterpretation.

What is claimed is:
 1. An apparatus comprising: a light source thatgenerates an exposing light; a first lens placed perpendicular to anoptical axis, said first lens having a front focal plane and a pupilplane; a binary mask placed perpendicular to said optical axis andbetween said light source and said first lens, said binary mask placedat said front focal plane of said first lens; a pupil filter placedperpendicular to said optical axis and at said pupil plane, said pupilfilter formed in accordance with: Pupil Filter=1−{[2(b−a)A ₁ sinc(kp(b−a)/2)cos(kp(a+b)/2)]/2a sin c(kpa)},  where A₁ is thetransmission amplitude of said binary mask, λ is the wavelength of saidexposing light, k=2Π/λ, a is one-half of a feature size of said binarymask, p is the pitch of said binary mask, and b=p/2; and a second lensplaced perpendicular to said optical axis, said second lens having afront focal plane at substantially the same position as said pupilplane, said second lens also having a back focal plane.
 2. The apparatusof claim 1 further including a semiconductor wafer placed at the backfocal plane of said second lens.
 3. The apparatus of claim 1 wherein thedistance between said pupil filter and said first lens is substantiallyequal to the focal length of said first lens, and the distance betweensaid pupil filter and said second lens is substantially equal to thefocal length of said second lens.
 4. The apparatus of claim 1 whereinsaid pupil filter acts to suppress the zero order of light passingthrough said binary mask.
 5. An apparatus comprising: a light sourcethat generates an exposing light; a first lens placed perpendicular toan optical axis, said first lens having a front focal plane and a pupilplane; a binary mask placed perpendicular to said optical axis andbetween said light source and said first lens, said binary mask placedat said front focal plane of said first lens; a pupil filter placedperpendicular to said optical axis and at said pupil plane, said pupilfilter formed such that the combination of said pupil filter, said firstlens, and said binary mask modify said exposing light to emulate theeffect of an attenuated phase shift mask version of said binary filterand said first lens acting on said exposing light, said pupil filterformed in accordance with: Pupil Filter=1−{[2(b−a)A ₁sinc(kp(b−a)/2)cos(kp(a+b)/2)]/2 a sin c(kpa)},  where A₁ is thetransmission amplitude of said binary mask, λ is the wavelength of saidexposing light, k=2Π/λ, a is one-half of a feature size of said binarymask, p is the pitch of said binary mask, and b=p/2; and a second lensplaced perpendicular to said optical axis, said second lens having afront focal plane at substantially the same position as said pupilplane, said second lens also having a back focal plane.
 6. The apparatusof claim 5 wherein said pupil filter acts to suppress the zero order oflight passing through said binary mask.
 7. The apparatus of claim 5further including a semiconductor wafer placed at the back focal planeof said second lens.
 8. The apparatus of claim 5 wherein the distancebetween said pupil filter and said first lens is substantially equal tothe focal length of said first lens, and the distance between said pupilfilter and said second lens is substantially equal to the focal lengthof said second lens.
 9. A method comprising: forming a pupil filter inaccordance with: Pupil Filter=1−{[2(b−a)A ₁ sinc(kp(b−a)/2)cos(kp(a+b)/2)]/2a sin c(kpa)},  where A₁ is thetransmission amplitude of said binary mask, λ is the wavelength of saidexposing light, k=2Π/λ, a is one-half of a feature size of said binarymask, p is the pitch of said binary mask, and b=p/2.
 10. The method ofclaim 9 further comprising placing said pupil filter at the pupil planeof first lens.
 11. The method of claim 10 further comprising placing abinary mask at front focal plane of said first lens.
 12. The method ofclaim 11 further comprising providing incident light onto said binarymask such that said incident light is selectively passed through saidbinary mask, said first lens, and said pupil filter.
 13. The method ofclaim 12 further comprising placing a second lens having a front focalplane and an image plane such that front focal plane substantiallycoincides with said pupil plane.
 14. The method of claim 13 furthercomprising placing a semiconductor wafer at said image plane.